Engineering reference for Indian students

Geotechnical

Soil Mechanics

5 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Index Properties of Soil
Draw the three-phase diagram and express void ratio, water content, degree of saturation and unit weight through the fundamental relation γ = (G + Se)γ_w/(1 + e); most numericals fall out once the phases are set.
Permeability and Seepage
Use Darcy’s law q = kiA with the hydraulic gradient i = Δh/L; for two-dimensional problems draw a flow net and compute seepage as q = kH(N_f/N_d).
$Critical hydraulic gradient i_{cr} = \frac{(G-1)}{(1+e)} for quick sand$
Compaction and Consolidation
Keep compaction (immediate mechanical densification giving maximum dry density at the optimum moisture content) distinct from consolidation (slow expulsion of pore water), and use T_v = C_v t/H_d² to link consolidation time to settlement.
$Zero air voids line: w = \frac{\gamma_{w}}{(G \gamma_{d})} - \frac{1}{\gamma_{d}}$
Shear Strength of Soil
Apply the Mohr-Coulomb criterion τ = c + σ tan φ (or the effective-stress form with σ′ = σ − u), obtaining c and φ from the Mohr circles of triaxial or direct shear tests.
$\phi = 0 analysis for saturated clay short-term stability$
Earth Pressure Theories
Pick the coefficient for the wall movement — active K_a = tan²(45 − φ/2) if the wall moves away, passive K_p = tan²(45 + φ/2) if it pushes into the soil — then integrate the pressure over the height to get the thrust P = ½KγH².